Predistortion circuit for a transmit system

ABSTRACT

Systems and methods related to amplifier systems which use a predistortion subsystem to compensate for expected distortions in the system output signal. A predistortion subsystem receives an input signal and applies a predistortion modification to the input signal. The predistortion modification may be a phase modification, a magnitude modification, or a combination of both. The predistorted signal is then received by an amplifier subsystem. The amplifier subsystem decomposes the predistorted signal into separate components, each having a constant envelope phase modulation, and separately amplifies each component. The phase modulated and amplified components are then recombined to arrive at an amplitude and phase modulated and amplified output signal. The predistortion modification is applied to the input to compensate for distortions introduced in the signal by the amplifier subsystem.

FIELD OF THE INVENTION

The present invention relates generally to power amplification systemsand is specifically applicable but not limited to power amplificationsystems using a Chireix architecture.

BACKGROUND OF THE INVENTION

The recent revolution in communications has caused a renewed focus onwireless technology based products. Mobile telephones, handheldcomputers, and other devices now seamlessly communicate using wirelesstechnology. One component that forms the core of such technology is theamplifier. Wireless devices require high efficiency amplifiers to notonly extend the range of their coverage but also to conserve the limitedbattery power that such devices carry.

One possible architecture which may be used for such a power amplifieris called a Chireix architecture. Named after Henry Chireix who firstproposed such an architecture in the 1930s, the Chireix architecture hasfallen out of favor due to its seemingly inherent limitations. However,it has recently been revisited as it provides some advantages that otherarchitectures do not have.

While the Chireix architecture provides some advantages, the processwhich the input signal undergoes also introduces some drawbacks.Specifically, distortions are introduced into the signal by thecomponents in the Chireix based amplifier/modulator system.

Based on the above, there is therefore a need for an amplifier systemwhich provides the benefits of a Chireix based amplifier but which alsocompensates for or avoids the distortions which a Chireix basedamplifier introduces. It is therefore an object of the present inventionto provide alternatives which mitigate if not overcome the disadvantagesof the prior art.

SUMMARY OF THE INVENTION

The present invention provides systems and methods related to amplifiersystems which use a predistortion subsystem to compensate for expecteddistortions in the system output signal. A predistortion subsystemreceives an input signal and applies a predistortion modification to theinput signal. The predistortion modification may be a phasemodification, a magnitude modification, or a combination of both. Thepredistorted signal is then received by an amplifier subsystem. Theamplifier subsystem decomposes the predistorted signal into separatecomponents, each having a constant envelope phase modulation, andseparately amplifies each component. The phase modulated and amplifiedcomponents are then recombined to arrive at an amplitude and phasemodulated and amplified output signal. The predistortion modification isapplied to the input to compensate for distortions introduced in thesignal by the amplifier subsystem.

In a first aspect, the present invention provides a system forprocessing an input signal, the system comprising:

-   -   a predistortion subsystem for receiving said input signal and        for producing a predistorted signal by applying a deliberate        predistortion to said input signal; and    -   a signal processing subsystem receiving and processing said        predistorted signal and producing a system output signal,        wherein    -   said predistortion subsystem distorts said input signal to        compensate for distortions in said system output signal;    -   said signal processing subsystem decomposes said predistorted        signal into separate components, each of said separate        components being processed separately; and    -   said processing subsystem combines said components after        processing to produce said system output signal.

In a second aspect the present invention provides a method of processingan input signal to produce a system output signal, the methodcomprising:

-   -   a) receiving said input signal    -   b) applying a deliberate predistortion to said input signal to        result in a predistorted signal    -   c) decomposing said predistorted signal into at least two        component signals    -   d) combining said at least two component signals to produce said        system output signal.

BRIEF DESCRIPTION OF THE DRAWINGS

A better understanding of the invention will be obtained by consideringthe detailed description below, with reference to the following drawingsin which:

FIG. 1 is a block diagram of a Chireix architecture amplifier subsystem;

FIG. 2 is a block diagram of an amplifier system using the subsystem ofFIG. 1 and a predistortion subsystem;

FIGS. 3A and 3B illustrate characteristics of distorted system outputsignals superimposed on the desired system output signalcharacteristics;

FIGS. 4A and 4B illustrate the characteristics of FIGS. 3A and 3B withcharacteristics of predistorted input signals;

FIG. 5 is a detailed block diagram of an amplifier subsystem accordingto the invention incorporating the Chireix amplifier subsystem of FIG. 1with a predistortion subsystem; and

FIG. 6 is a block diagram of a signal processing system according toanother embodiment of the invention.

DETAILED DESCRIPTION

For clarity, the following terms are to be used with the followingdefinitions:

-   -   AM (amplitude modulation) refers to the AM of an RF (radio        frequency) signal and is equal to the magnitude of the RF        signal's complex base band equivalent    -   PM (phase modulation) refers to the PM of an RF signal and is        equal to the phase of the RF signal's complex base band        equivalent.

Referring to FIG. 1, a block diagram of a Chireix architecture amplifiersubsystem 10 is illustrated. A signal decomposer 20 receives an inputcomplex baseband signal 30. Phase modulated RF signals 80A, 80B areproduced after the decomposed output of the decomposer 20 are phasemodulated by phase modulation circuitry 85A, 85B. These phase modulatedsignals 80A, 80B are received by power amplifiers 90A, 90B. The phasemodulated signals are thus amplified by the power amplifiers 90A, 90Band are received by a signal combiner 100. The system output signal 110(an RF signal corresponding to the input baseband signal 30) is outputfrom the combiner 100 and is an amplified and modulated version of theinput signal 30. Phase modulation of the phase modulated signals 80A,80B is executed after the signal decomposer 20 separates input signal 30into at least two components. These at least two components, after phasemodulation, are the signals 80A, 80B.

As noted above, the Chireix architecture amplifier subsystem 10 has beenknown to introduce distortions in the system output signal 110. Tocompensate for such distortions, a predistortion subsystem 120 isprovided. Referring to FIG. 2, the predistortion subsystem 120 receivesthe input signal 30 and produces a predistorted signal 130. Thepredistorted signal 130 is received by the amplifier subsystem 10. Theamplifier subsystem then produces the system output signal 110.

The distortions for which the predistortion subsystem is to compensatemay come as a phase distortion, a magnitude distortion, or as acombination of both. It has been found that, without predistortion, thesystem output signal has an amplitude modulation (AM) envelope that isnot equal to the expected and desired AM envelope. Furthermore, thephase modulation (PM) of the system output signal 110, if predistortionis not present, deviates from the expected and desired PM. Experimentshave found that the AM distortion or error (magnitude distortion) of thesystem output signal 110 depends on the AM of the input signal. Also, ithas been found that the PM distortion (or phase distortion) of thesystem output signal 110 depends on the AM of the input signal 30.

To further explain the above, FIGS. 3A, 3B are provided. As can be seenin FIG. 3A, the desired AM characteristic 140 is not followed by theresulting AM 150 of the system output signal. There is a 10% error ordeviation in the middle segment of the waveform 150 from the desired AMcharacteristic 140. For FIG. 3B, the resulting PM 160 of the systemoutput signal deviates from the desired PM characteristic (in this case0°) as the AM varies. These distortion effects have been found to becaused by the Chireix architecture components.

While the above problems in distortion have been caused by the Chireixarchitecture, one solution is to compensate for the distortion bypredistorting the input signal. As an example, if it is known that theamplifier subsystem will cause a PM distortion of x degrees at an AM ofy, then predistorting the input signal by −x degrees at an AM of yshould produce a system output signal with no PM distortion. The sameprinciple can be applied for the AM distortion. If it is known that fora given input signal AM of a, the resulting system output signal willhave an AM distortion of b, then predistorting the input signal in amanner which results in an output AM distortion of 0 negates theundesired effects of the AM distortion. This concept is illustrated inFIGS. 4A and 4B.

Referring to FIGS. 4A and 4B, illustrated are the desired AMpredistortion output characteristic 170 and the desired PM predistortionoutput characteristic 180. In FIG. 4A, since the resulting AMcharacteristic 150 (with no predistortion) is distorted, thenpredistortion which results in the AM predistorted output characteristic170 should produce the desired PM characteristic 140. Similarly, in FIG.4B, the distortion of the resulting PM characteristic 160 (with nopredistortion) can be compensated for by providing predistortion thatresults in a PM predistorted output characteristic 180. By specificallypredistorting the input signal by the amount of the expected distortion,the resulting system output signal should be generally free of AM/AM andAM/PM distortions.

It should be noted that the predistortion modification, defined as anydeliberate distortion which has been applied or is to be applied to theinput signal to change at least one original characteristic of the inputsignal, can take many forms. Two specific types of predistortion, phasepredistortion and magnitude predistortion are currently envisionedalthough other types are possible. These two types, separately ortogether, can make up the predistortion modification. In someapplications, only a magnitude type predistortion modification may berequired while in others only a phase type predistortion is required.

The predistortion discussion above can be implemented in thepredistortion subsystem 120 illustrated in FIG. 2. A more detailedillustration of the predistortion subsystem 120 is presented in FIG. 5.While an analog implementation of the predistortion subsystem ispossible, it has been found that a digital implementation was simpler toachieve. As can be seen in the embodiment illustrated in FIG. 5, thepredistortion subsystem 120 has 4 main components: a Cartesian to polarconversion unit 190, a magnitude lookup table 200 (magnitude LUT), aphase lookup table 210 (phase LUT), and an adder 220. The input signalis received by the conversion unit 190 and is converted from Cartesiancoordinates to polar coordinates. The converted signal is then receivedand used by the lookup tables 200, 210 to determine the proper amount ofpredistortion to be applied. The phase lookup table 210 provides theamount of phase distortion to be added to the phase value 214 by way ofadder 220. The magnitude LUT 200 provides the desired value of thepredistorted magnitude. This desired value is then substituted with themagnitude value received from the conversion unit 190. As can beunderstood from above, the magnitude value 212 received from theconversion unit 190 is determinative of the amount of predistortionrequired for both magnitude and phase. The predistorted signal is thenpassed on to the amplifier subsystem 10. For a better understanding ofFIG. 5, it should be kept in mind that the input signal 30 is a digitalsignal having a digital representation of its AM envelope and of its PM.

The conversion unit 190, while present, is not necessary but merelyconvenient and makes the predistortion easier to accomplish. As is wellknown, signal representations using Cartesian coordinates take the formof z=x+jy where x and y are the real and imaginary components. Polarcoordinates take the form of z=Ae^(jφ) where the magnitude of the signalis A and its phase is φ. Since both the magnitude and the phase of thesignal is to be modified by the predistortion subsystem, it is clearlymore convenient to accomplish this if the signal were in polarcoordinates. Again as is well known, A=(x²+y²)^(1/2) while φ=tan⁻¹(y/x). Once the signal has been converted into polar coordinates,adjusting the magnitude is as simple as replacing the digitalrepresentation of A by another number. Similarly, the phase can beadjusted by adding a phase correction to the phase of the signal.

After the digital signal is received and converted by the conversionunit 190, the signal is now represented by two values—a magnitude value212 and a phase value 214. As noted above, the magnitude of the signalis determinative of the distortion of the system output signal. As such,FIG. 5 illustrates the different signal paths followed by these twovalues—one path for the magnitude value 212 and a second path for thephase value 214.

As noted above, the magnitude value 212 can be easily replaced by thedesired magnitude value. This is done by way of magnitude lookup tableblock 200. The lookup table internal to the magnitude lookup table block200 represents an input/output relationship with the input being thedesired magnitude and the output being the predistorted signalmagnitude. Thus, if the magnitude LUT block 200 has a table entry withan input value of 0.5 and an output value of 0.4, then if theundistorted magnitude value received by the magnitude LUT block 200 is0.5, then this value is replaced with 0.4 as the output of the magnitudeLUT block 200. Based on the LUT (lookup table) entries, the magnitude ofthe undistorted signal is therefore replaced with the desiredpredistorted magnitude.

Similar to the above, the phase value of the converted input signal isadjusted as well. As can be seen in FIG. 5, the magnitude value 212 isalso received by the phase lookup table block 210. The phase lookuptable block 210, based on the magnitude value, determines the properamount of phase adjustment and adds this phase adjustment to the phasevalue 214 by way of the adder 220. The phase lookup table block 210 alsohas an lookup table resident within the phase LUT block 210 that detailsthe appropriate phase adjustments for given magnitude values.

While the above described magnitude LUT replaces a desired value for thereceived magnitude, other implementations are possible. Instead of adirect replacement value, the magnitude LUT may provide a correctivevalue to the received magnitude. This corrective value can, depending onthe implementation, be an additive or a multiplicative corrective value.

It should be noted that the lookup table entries found in the lookuptables internal to the magnitude LUT block 200 and the phase LUT block210 may be based on experimentally derived data. As an example of howsuch experimentally derived data can be found, a desired output valuefrom the amplifier subsystem 10 is first chosen. Then, an input signalto the amplifier subsystem 10 is adjusted until the desired output valueis achieved. That is, if it is found that a value of q input to theamplifier subsystem 10 produces a desired amplifier output value of t,then, in the lookup table the value of q is entered as the value to beoutput from the lookup table block for a desired value t. For themagnitude table, the desired amplifier output value is entered as thevalue to be input to the lookup table block. As such, if a value of t isinput to the magnitude LUT block 200, a value of q is output from theblock 200 to produce an amplifier output value of t. The table entriescan be found by adjustments of the entries until the desired output isobtained.

For the phase table, if experimentation shows that an input magnitude214 of r results in a distortion of s in the phase, then the correctivevalue can easily be found. As such, the phase table would, for an inputvalue 212 corresponding to the magnitude r, contain the correctivevalue. Again, the table entries can be adjusted.

It should be noted that the above is provided merely as an example.Other methods for filling the table with the correct entries may beemployed.

As an example, such lookup tables may have the following entries:

Input AM Magnitude AM Predistortion Value IN1 AM1 IN2 AM2 IN3 AM3 InputAM Magnitude Phase Predistortion Adjustment IN1 PM1 IN2 PM2 IN3 PM3Thus, if the amplifier system detects the input AM magnitude as IN1,then the AM predistorted magnitude should have a value of AM1 and thephase predistortion should have an added value of PM1. Thus, forpredistortion, the input AM magnitude of IN1 is replaced by a value ofAM1. Similarly, if the input phase is PM0, then for an input AMmagnitude of IN1, then the resulting predistorted phase should bePM0+PM1.

The magnitude and phase correction concept can be further refined, ifapplicable, by using a polynomial to determine the requiredpredistortion. If a mathematical relationship is found to approximate orequate the relationship between the input (such as input magnitude orinput phase) and the required predistortion, this mathematicalrelationship can be used to generate the predistortion.

It should be noted that if the magnitude value of the input signal isnot found in the lookup tables, interpolation may be used to formulatethe required predistortion value. The interpolation may be linear forsimplicity in implementation or it may be a more complex form ofinterpolation. As an example of linear interpolation, if the magnitudevalue is 0.45 while the magnitude lookup table only had predistortionentries for 0.4 and 0.5, then the midpoint value for the correspondingpredistortion entries may be used. In this case, if the predistortionentry for a magnitude value of 0.4 is 0.3 and the predistortion entryfor a magnitude value of 0.5 is 0.4, then the average between the twopredistortion entries may be used, (i.e. (0.3+0.4)/2=0.35) as thepredistortion value to be used. Of course while such simple linearinterpolation may be used, more complex interpolation schemes, such asthose using different weight values for different table entries, may beused.

It should also be clear that the circuit of FIG. 5 contains featuresrelating to one embodiment of the amplifier subsystem. In FIG. 5, thesignal decomposer 20 of FIG. 1 contains a phasor fragmentation engine20A. The fragmentation engine 20A receives the magnitude (M) and phase(φ)) representing the predistorted signal. The phasor fragmentationengine 20A deconstructs a predetermined modulation waveform (thepredistorted signal) into signal components which are of equalmagnitude. Further information regarding the phasor fragmentationengines may be found in the applicant's co-pending application U.S.application Ser. No. 10/205,743 entitled COMPUTATIONAL CIRCUITS ANDMETHODS FOR PROCESSING MODULATED SIGNALS HAVING NON-CONSTANT ENVELOPES,which is hereby incorporated by reference. In FIG. 5, these signalcomponents are denoted by angles α and β. These components are eachreceived by phase modulation and filtering blocks 60A, 60B which processthe components to produce phase modulated and filtered versions of thecomponents. The signal component 70A is an RF signal with phase α whilesignal component 70B is an RF signal with phase β. These components 70A,70B are then amplified by amplifiers 90A, 90B. The amplified componentsare then recombined using combiner 100. Signal decomposition methodsother than the phasor fragmentation referred to above may also be usedby the signal decomposer 20.

Regarding the Chireix architecture amplifier subsystem 10, it has beenfound that, for higher amplification efficiencies, switch modeamplifiers are preferred for the amplifiers 90A, 90B. Such switch modeamplifiers, specifically Class D and Class F power amplifiers, providelow output impedances that allow higher amplification efficiencies. Aco-pending application filed on Oct. 16, 2002 and having U.S. Ser. No.10/272,725 entitled CHIREIX ARCHITECTURE USING LOW IMPEDANCE AMPLIFIERSprovides further information on the desirable components and is herebyincorporated by reference. Such types of amplifiers are not required forthe invention to function but they have been found to provideperformance at a desirable level.

It should further be noted that while there are only two parallelamplifiers 90A, 90B in FIG. 1 and FIG. 5, multiple parallel amplifiersmay be used as long as the decomposer 20 decomposes the predistortedsignal 130 into enough components so that each component is separatelyamplified and phase modulated in parallel with the other components.

As another alternative, while FIG. 5 illustrates a parallelimplementation of the predistortion, a serial implementation ispossible. As can be seen in FIG. 5, the magnitude predistortion isapplied in parallel with the phase predistortion. While this ispreferable for purposes of speed, it is also possible to have cascadedpredistortion stages. A magnitude predistortion can be applied to theinput signal after first applying a phase predistortion.

It should also be noted that the predistortion subsystem 10 explainedabove does not linearize a power amplifier as is well-known in thefield. Instead, the predistortion subsystem linearizes a whole poweramplifier system—the output of the whole amplifier system is linearizedand not simply the output of a single amplifier. Also, unlike thelinearizing systems for power amplifiers that are currently known, theamplifier system discussed in this document compensates for distortionsthat mostly occur at mid signal amplitudes. Current single amplifierlinearization systems linearize distortions that occur at large signalamplitudes.

It should further be noted that the invention may be applied to anysignal processing system which decomposes a signal into components andrecombines them. It has been found that signal combiners (block 100 inFIG. 1) invariably cause distortions. These combiners use addition torecombine the components and improper signal addition, such as whenrecombining sinusoidal components, has been found to be one cause of thedistortions in the system output signal. In the above embodiment, thephasor fragmentation engine decomposes the incoming signal into vectorsand the improper addition of these vectors by the combiner 100 lead todistortions in the output signal.

While the above embodiment amplifies the input signal, albeit separatelyfor each component, this need not be the only signal processingaccomplished after the input signal is decomposed. Referring to FIG. 6,such a generalized system 10A (which may be part of a larger signaltransmission system) is illustrated. The predistortion subsystem 120predistorts an incoming signal 30 and compensates for distortionsintroduced in the system output signal 110 by the improper or imperfectrecombining of the input signals components. These components areproduced by the signal decomposer 20 and are separately processed bysignal component processor blocks 75A, 75B. The processing executed bythe blocks 75A, 75B may take the form of amplification (as in theembodiment above), phase modulation, a combination of the two, or anyother signal processing which may be desired. As an example, each of thesignal components illustrated in FIG. 5 may be separately phasemodulated in addition to being amplified by amplifiers 90A-90B. Thephase modulation may be accomplished separately or be incorporated inthe signal decomposer or, as contemplated for the implementationillustrated in FIG. 5, incorporated into the modulation and filteringblocks 60A, 60B.

As can be seen in FIG. 6, the signal processing subsystem 10A receivesthe predistorted signal from the predistortion subsystem 120. Afterbeing received, the predistorted signal is decomposed by the signaldecomposer 20 into components. These components are then separatelyprocessed by the signal component processor blocks 75A, 75B and are thenrecombined by the recombiner 100.

One advantage using the above invention is that it allows less stringenttolerances to be used for the system components. Previously, componentshad to be substantially matched so that signal processing could produceacceptable results. By using the above invention, less thansubstantially matched components may be used together. Errors due to amismatch may be measured and compensated for by the predistortionsubsystem.

A person understanding this invention may now conceive of alternativestructures and embodiments or variations of the above all of which areintended to fall within the scope of the invention as defined in theclaims that follow.

1. A system for processing an input signal, the system comprising: apredistortion subsystem adapted to receive said input signal and adaptedto produce a predistorted signal by applying a deliberate predistortionto said input signal, wherein said predistortion subsystem is adapted todistort said input signal to compensate for distortions in a systemoutput signal; and a signal processing subsystem adapted to receive andprocess said predistorted signal and adapted to produce said systemoutput signal, wherein said signal processing subsystem is adapted todecompose said predistorted signal into at least two components, each ofsaid at least two components being processed separately, said signalprocessing subsystem adapted to combine said at least two componentsafter processing to produce said system output signal, and wherein saidsignal processing subsystem comprises a signal decomposer adapted todecompose said predistorted signal into said at least two components, atleast two signal component processor blocks, each of said at least twosignal component processor blocks including a respective amplifier, eachof said signal component processor blocks adapted to receive arespective one of said at least two components from said signaldecomposer, and each of said signal component processor blocks adaptedto separately process said respective one of said at least twocomponents and to produce a respective processed output, and a combineradapted to receive said respective processed outputs from each of saidat least two signal component processor blocks, said combiner producingsaid system output signal from said respective processed outputs of saidat least two signal component processor blocks; wherein saidpredistorted signal is represented as a sequence of magnitude and phasepairs; and wherein said signal decomposer includes a phasorfragmentation engine to receive said sequence of magnitude and phasepairs, said phasor fragmentation engine adapted to decompose saidpredistorted signal into said at least two components, each of said atleast two components exhibiting a respective magnitude and having arespective varying phase, said respective magnitudes of at least two ofsaid at least two components being substantially equal.
 2. The systemaccording to claim 1 wherein said respective amplifier comprises anon-linear amplifier.
 3. The system according to claim 1 wherein saidsystem is part of a signal transmission system.
 4. The system accordingto claim 1 wherein at least some of said distortions are due to saidcombiner.
 5. The system according to claim 1 wherein said respectiveamplifier comprises a switch mode amplifier.
 6. The system according toclaim 1 wherein said respective amplifier has a low-output impedance. 7.The system according to claim 1 wherein said deliberate predistortionincludes magnitude distortions adapted to adjust a magnitude of saidinput signal.
 8. A The system according to claim 1 wherein saiddeliberate predistortion includes phase distortions adapted to adjust aphase of said input signal.
 9. The system according to claim 1 whereinsaid deliberate predistortion is based on at least one entry in a lookuptable.
 10. A method of processing an input signal to produce a systemoutput signal, the method comprising: receiving said input signal;predistorting, via applying a deliberate predistortion, said inputsignal to provide a predistorted signal represented as a sequence ofmagnitude and phase pairs; decomposing said predistorted signal into atleast two component signals; separately processing each of said at leasttwo component signals, wherein said processing further includesamplifying each of said at least two component signals; and combiningsaid at least two component signals to produce said system outputsignal; wherein said decomposing comprises receiving said sequence ofmagnitude and phase pairs and producing therefrom said at least twocomponent signals, each of said at least two component signalsexhibiting a respective magnitude and having a respective varying phase,said respective magnitudes of at least two of said at least twocomponent signals being substantially equal; and wherein saiddecomposing comprises converting said sequence of magnitude and phasepairs into two parallel sequences of phasors representing said at leasttwo component signals, each of said phasors at a respective phase andsubstantially equal in magnitude to Vmax/2; and wherein Vmax is amaximum amplitude of said predistorted signal over a period of saidsequence of magnitude and phase pairs.
 11. The method according to claim10 wherein said system output signal is an RF modulated version of saidinput signal.
 12. The method according to claim 10 wherein saidprocessing includes phase modulating at least one of said at least twocomponent signals.
 13. The method according to claim 10 wherein saidreceiving further includes accessing an entry in a lookup table, saiddeliberate predistortion being based, at least in part, on said entry.14. The method according to claim 13 wherein said deliberatepredistortion is based on an interpolation of entries in said table. 15.The system according to claim 9 wherein said deliberate predistortion isbased on an interpolation of entries in said table.
 16. A systemaccording to claim 1 wherein said phasor fragmentation engine isconfigured to convert said sequence of magnitude and phase pairs intotwo parallel sequences of phasors representing said at least twocomponents, each of said phasors at a respective phase and substantiallyequal in magnitude to Vmax/2; and wherein Vmax is a maximum amplitude ofsaid predistorted signal over a period of said sequence of magnitude andphase pairs.
 17. A system according to claim 16 wherein said phasorfragmentation engine is adapted to determine the respective phases of aparticular pair of said phasors derived from a particular one of saidsequence of magnitude and phase pairs as θ−φ and θ+φ respectively; andwherein V and θ are a respective magnitude and a respective phase ofsaid particular one of said sequence of magnitude and phase pairs, andφ=cos⁻¹(V/Vmax).
 18. A system according to claim 1 wherein saidrespective amplifier comprises a class D amplifier.
 19. A methodaccording to claim 10 wherein said decomposing determines the respectivephases of a particular pair of said phasors derived from a particularone of said sequence of magnitude and phase pairs as θ−φ and θ+φrespectively; and wherein V and θ are a respective magnitude and arespective phase of said particular one of said sequence of magnitudeand phase pairs, and φ=cos⁻¹(V/Vmax).